Local damage and crack band model for concrete

In order to eliminate the element size dependence of the cracking finite element analysis on concrete, a local damage and crack band model was proposed within the material nonlinear finite element analysis framework using local constitutive models. The requirement of adjusting the stress and strain relations under different element sizes can be satisfied by using the power-type tensile damage evolution equation with three parameters. The stress and crack strain relations under different element sizes, which can ensure the objectivity of the fracture energy, can be obtained on the basis of the original stress and crack strain by introducing the fracture energy and the crack band width related to the element size into the local damage constitutive model. Moreover, an optimization inversion approach employing the asynchronous particle swarm intelligent algorithm was proposed to adaptively determine the model parameters based on the stress and crack strain relation related to element size. The proposed model was implemented in ABAQUS, and the effectiveness of the model and the correctness of programming were validated.